I'm curious how badly the pro-slavery side was losing in the political process that it made secession an attractive option.
Is there a particular bill you have in mind? There were no bills for emancipating slaves before Congress in 1860 when Southern states began to secede.
South Carolina's secession was precipitated by the Republican victory in the 1860 elections, and the perceived threat this created for the expansion of slavery.
But as far as I am aware, Congress did not take up any bills to end slavery until it passed the 13th Amendment in 1865 (with no Southern members present, for obvious reasons).